Consider the demand function $X(p)=\dfrac{1}{(p-2)^2}+3$, $(p>2)$. Determine the elasticity of the inverse demand function at $X=4$. Here, you may use that $X(3)=4$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$-\frac{3}{2}$.
Antwoord 2 correct
Fout
Antwoord 3 optie
$-2$
Antwoord 3 correct
Fout
Antwoord 4 optie
$-\frac{1}{2}$
Antwoord 4 correct
Fout
Antwoord 1 optie
$-\frac{2}{3}$
Antwoord 1 feedback
Correct: $\epsilon^X=X'(p)\cdot \dfrac{p}{X(p)}$.
$X'(p)=-\dfrac{2}{(p-2)^3}$.
Hence, $\epsilon^X=-\dfrac{2}{(p-2)^3}\cdot \dfrac{p}{\frac{1}{(p-2)^3}+3}$.
At $p=3$: $\epsilon^X=-\frac{3}{2}$.
So, at $X=4$: $\epsilon^p=\frac{1}{\epsilon^X}=\frac{1}{-\frac{3}{2}}=-\frac{2}{3}$.
Go on.
$X'(p)=-\dfrac{2}{(p-2)^3}$.
Hence, $\epsilon^X=-\dfrac{2}{(p-2)^3}\cdot \dfrac{p}{\frac{1}{(p-2)^3}+3}$.
At $p=3$: $\epsilon^X=-\frac{3}{2}$.
So, at $X=4$: $\epsilon^p=\frac{1}{\epsilon^X}=\frac{1}{-\frac{3}{2}}=-\frac{2}{3}$.
Go on.
Antwoord 2 feedback
Wrong: You have to find the elasticity of the inverse demand function.-2-2h
See Applications 2: Elasticity and inverse.
See Applications 2: Elasticity and inverse.
Antwoord 3 feedback
Antwoord 4 feedback